Linear Graphs and Equations 2

1
Linear Graphs and Equations (2)

• Recap
• Sketching linear graphs
• Identifying graphs
• Parallel Lines
• Perpendicular Lines

2
Gradient

• Gradient tells us how steep something is.

This child doesnt have a clue about gradient.
3
Gradient
What is the gradient of the line?
Gradient 5/2 or 2.5
4
Gradient
What is the gradient of this line?
This time there is a decrease in y
Gradient -2/4 or -0.5
5
Linear graphs
y - intercept
Gradient
6
Different Linear graphs
y 6 9x
2y 2 x/6
3x 3y 11
y/4 x/3
y 3 5(x - 5)
4(y 1) (x - 9)/11
No Indices (i.e. powers of x or y) No
Reciprocals (e.g. 1/x) No combinations of x and y
(e.g. 3xy x 2) No other functions (e.g. y
sin(x) y ex)
notice what they have in common
7
Sketching Linear Graphs
What is y when x is 0?
What is x when y is 0?
We can now use this to get two sets of
coordinates.
8
Sketching Linear Graphs
We know that our line must go through the points
(0,-4) and (2,0)
To draw a sketch of this graph, we just need to
label the important points.
9
Activity 1

• Time allowed 8 minutes
• Turn to page 6 of your Core 1 book and answer
  question A3, and A5.

10
Gradient

• Find the gradient of the straight line graph
  3x2y-70

• Put into the form y mx c

• What is the y intercept?

• Write down the equation of a straight line that
  is parallel to this one.

11
Parallel Lines
If two lines with gradients m1 and m2 are
parallel, then
E.g. y 3x 1 and y 3x - 3 E.g. y
-x -1 and y -x 54
12
Activity 2

• Time allowed 4 minutes
• Turn to page 7 of your Core 1 book and answer
  question A7

13
Perpendicular lines
What is the gradient of the blue line?
What is the gradient of the red line?
Draw a line with a gradient of 5. Now draw a
perpendicular line to this one. What is the
gradient of this line?
Is there a relationship???
14
Perpendicular Lines
If two lines with gradients m1 and m2 are
perpendicular, then
15
Activity 3
Which of the following are perpendicular to y
5x 2 ?
16
Activity 4

• Time allowed Rest of lesson
• Turn to page 8 of your Core 1 book and answer
  question A10, A11, A12
• Homework Exercise A (page 9)
• Questions 1, 2, 4, 8